## GrizzlyChicken 3 years ago how do you solve 16^(-3/4) without a calculator?

1. 009infinity

split the powers and then do individually

2. GrizzlyChicken

what do you mean by split the powers?

3. 009infinity

do u got it

4. GrizzlyChicken

no, im lost where -3 is multiplyed by 6 and then the ^1/4 part

5. 009infinity

ok i explain in steps

6. theEric

(-3) means $\frac{1}{16^3}$ and (1/4) means $\sqrt[4]{16}$ right? So, since you're doing both to the 16... it can be written as $\frac{1}{\sqrt[4]{16^3}}$ or $\frac{1}{\sqrt[4]{16}^3}$

7. GrizzlyChicken

that makes sense so far

8. theEric

Now, one looks much more easy to solve than the other, even though they are the same thing.

9. 009infinity

the power is -3/4 base is 16 now 16^-3 . 16^1/4=1/(16)^3.$\sqrt[4]{16}$

10. GrizzlyChicken

how does $\sqrt[4]{16^3}$ turn into 8?

11. GrizzlyChicken

i know the answer is 1/8

12. GrizzlyChicken

$\sqrt[4]{4096}$

13. GrizzlyChicken

nvm

14. theEric

I would look at it the other way - just to avoid that huge number $16^3$.

15. theEric

$\frac{1}{\sqrt[4]{16}^3}$

16. theEric

So it's like $\frac{1}{(\sqrt[4]{16})^3}$

17. theEric

And what is $\sqrt[4]{16}$?

18. theEric

Guess :P

19. theEric

It's a nice number.

20. GrizzlyChicken

2

21. GrizzlyChicken

sorry, i was afk for a while

22. GrizzlyChicken

then 2^3 is 8

23. GrizzlyChicken

so 1/8

24. GrizzlyChicken

thanks!

25. theEric

Understood! Thank you! And you're welcome!